www.michael-buhlmann.de
Funktion: f(x) = x2 + x - 6/x, Df = R\{0}, Wf = R, gebrochen rationale Funktion, x -> -∞: f(x) -> x2 + x = y als Grenzkurve, x -> +∞: f(x) -> x2 + x = y als Grenzkurve ->
| Wertetabelle: | |||||
| x | f(x) | f'(x) | f''(x) | f'''(x) | Besondere Kurvenpunkte |
| -10 | 90.6 | -18.94 | 2.01 | 0 | |
| -9.5 | 81.3816 | -17.93 | 2.01 | 0 | |
| -9 | 72.6667 | -16.93 | 2.02 | 0.01 | |
| -8.5 | 64.4559 | -15.92 | 2.02 | 0.01 | |
| -8 | 56.75 | -14.91 | 2.02 | 0.01 | |
| -7.5 | 49.55 | -13.89 | 2.03 | 0.01 | |
| -7 | 42.8571 | -12.88 | 2.03 | 0.01 | |
| -6.5 | 36.6731 | -11.86 | 2.04 | 0.02 | |
| -6 | 31 | -10.83 | 2.06 | 0.03 | |
| -5.5 | 25.8409 | -9.8 | 2.07 | 0.04 | |
| -5 | 21.2 | -8.76 | 2.1 | 0.06 | |
| -4.5 | 17.0833 | -7.7 | 2.13 | 0.09 | |
| -4 | 13.5 | -6.62 | 2.19 | 0.14 | |
| -3.5 | 10.4643 | -5.51 | 2.28 | 0.24 | |
| -3 | 8 | -4.33 | 2.44 | 0.44 | |
| -2.5 | 6.15 | -3.04 | 2.77 | 0.92 | |
| -2 | 5 | -1.5 | 3.5 | 2.25 | |
| -1.63 | 4.7079 | 0 | 4.77 | 5.11 | Tiefpunkt T(-1.63|4.71) |
| -1.5 | 4.75 | 0.67 | 5.56 | 7.12 | |
| -1 | 6 | 5 | 14 | 36.07 | |
| -0.5 | 11.75 | 24 | 98 | 578.32 | |
| 0 | Infinity | Infinity | Infinity | Infinity | Senkrechte Asymptote/Pol x = 0 mit Vorzeichenwechsel: x -> 0-: f(x) -> +∞, x -> 0+: f(x) -> -∞ |
| 0.5 | -11.25 | 26 | -94 | 573.71 | |
| 1 | -4 | 9 | -10 | 35.93 | |
| 1.5 | -0.25 | 6.67 | -1.56 | 7.1 | |
| 1.537 | 0 | 6.61 | -1.3 | 6.44 | Nullstelle N(1.54|0) |
| 1.817 | 1.8163 | 6.45 | 0 | 3.3 | Wendepunkt W(1.82|1.82) |
| 2 | 3 | 6.5 | 0.5 | 2.25 | |
| 2.5 | 6.35 | 6.96 | 1.23 | 0.92 | |
| 3 | 10 | 7.67 | 1.56 | 0.44 | |
| 3.5 | 14.0357 | 8.49 | 1.72 | 0.24 | |
| 4 | 18.5 | 9.38 | 1.81 | 0.14 | |
| 4.5 | 23.4167 | 10.3 | 1.87 | 0.09 | |
| 5 | 28.8 | 11.24 | 1.9 | 0.06 | |
| 5.5 | 34.6591 | 12.2 | 1.93 | 0.04 | |
| 6 | 41 | 13.17 | 1.94 | 0.03 | |
| 6.5 | 47.8269 | 14.14 | 1.96 | 0.02 | |
| 7 | 55.1429 | 15.12 | 1.97 | 0.01 | |
| 7.5 | 62.95 | 16.11 | 1.97 | 0.01 | |
| 8 | 71.25 | 17.09 | 1.98 | 0.01 | |
| 8.5 | 80.0441 | 18.08 | 1.98 | 0.01 | |
| 9 | 89.3333 | 19.07 | 1.98 | 0.01 | |
| 9.5 | 99.1184 | 20.07 | 1.99 | 0 | |
| 10 | 109.4 | 21.06 | 1.99 | 0 | |
| Graph: | |||||
| |||||
Graph(en) der Asymptote(n), Grenzkurve(n).
Abkürzungen: Df = (maximaler) Definitionsbereich, f(x) = Funktion, f'(x) = 1. Ableitung, f''(x) = 2. Ableitung, f'''(x) = 3. Ableitung, H = Hochpunkt, L = Lücke, N = Nullstelle, P = Polstelle, R = reelle Zahlen, S = Sprungstelle, T = Tiefpunkt, W = Wendepunkt, WS = Sattelpunkt, Wf = Wertebereich, {.} = ein-/mehrelementige Menge, [.; .] = abgeschlossenes Intervall, (.; .) = offenes Intervall, [.; .), (.; .] = halboffenes Intervall, ∞ = unendlich.
Bearbeiter: Michael Buhlmann